In the typical positive displacement rotary mechanism having two or more rotary lobes forming a compressor or vacuum pump or combustion engine, the lobes have surfaces paralleling the lobe axes and require the additional cooperation of either a surrounding housing to form the expansible and contractible working space (chamber) or intake and exhaust porting and valving in or on the lobes to communicate with the working space where the lobes independently define the outer periphery of the working space. Moreover, such prior mechanisms typically produce not more than one complete working cycle per lobe revolution.